Question

Please help me with #2.1

A coil composed of N turns of wire is placed inside a very long solenoid of n turns per unit length. I lo sin wt. Th was designed such that th (2.1) The si d's iht the wnat iS solenoid is connected to a power supply that sends a current to the solenoid given by e coil inside the solenoid has a cross-sectional area A and the coil is oriented such eld is perpendicular to the area (i.e., A is parallet to setenoid's field). The coil e area of the coil decreases linearly with time according to the equation: AC)Ao(1 - at) What is the emf induced in the coil?

Book: physics for scientists and engineers 4th edition knight

Answer 1

i = i_0 sin omega t A = A_0 (1 - alpha t) emf induced = E = ? d phi/dt = d/dt [B middot A] = d/ dt [mu_0 n i middot A_0 (1 - alpha t)] = d/ dt [mu_0 n i_0 middot sin omega t middot A_0 middot [1 - alpha t]] = mu_0 n i_0 A d/ dt [sin omega t - alpha t sin omega t] = mu_0 n i_0 A [t cos omega t - alpha [t cos omega t omega + sin omega t]] E = mu_0 n i_0 A [t cos omega t - alpha t omega cos omega t - alpha sin omega t] E = mu_0 n i_0 a [t cos omega t [1 - alpha omega] - alpha sin omega t]